112 Dr. G, H. Bryan and Mr. W. E. Williams. [Jan. 7, 



to be = 4a 2 . Substituting these values in the expressions for the 

 coefficients, we have 



mX u 



= 3 6KSV, 



mY u 



= 0-02KSV, 



mX v 



= 0-58KSV, 



mY v 



= -0-1KSV, 



mX e 



= l-8KSVo» 



mY e 



= 0-OOKSV, 



mG u 



= 2-61KSV« 3 



mG v 



= 0'44KSVa, 



mGe 



= 30KSW. 







Substituting again in the expressions for A, B, C, D, E, we obtain, 

 putting k 2 = 4a 2 , 



A = 4a 2 , B = 2390 ~, C = 142a- 13700 ~, 



V V- 



D = 2500^, E = 284000 * 

 V 



H is positive if V 2 > 2000a, which is the condition of stability for 

 this form of glider. 



By putting I = 7 "4a, I represents approximately the extreme length 

 of the glider, and the condition of stability reduces to V 2 > 270/. 



Ex. 6. — Consider next the case of two unequal square planes, 

 inclined at an angle, and in the first case suppose that the smaller 

 plane is in front. 



Let S and S' be the respective areas, and suppose S = 10S'. 



Let 2a be the breadth of the large plane, and 2«/3*l that of the 

 smaller, also let the distance between the centres be equal to 3a : and 

 let Jc 2 = a 2 . 



Let the angle a between the large plane and the direction of motion 

 be 10°, and let the angle between the two planes be also 10°, so that 

 the small plane is inclined at an angle of 20° to the direction of 

 motion. 



Then we have 



/(a) - 0-3, /'(a) = 1-6, 0(a) = 0-49, <£'( a ) = °' 59 > ' 



/(a + 0) = O-5, /'(a + j8) = 1*57, 0(a + /3) = O'4, f(a + j8) = 0-56. 



For equilibrium we have, if t] be the distance between e.g. and centre 

 of large plane, 



S/(a) (r, - a4(a)) = S'/(a + £)(& + a' (a + /?)- V ). 



Therefore rj = 0'94«, so that t]\ = b-r) = 2'0Qa. 



Substituting in the expressions for X u , etc., 

 mX u = 1-87 KSV, mX v = 0-41 KSV, mX e = 1-4 KSVa, 

 mG u = 0-57 KSVa, mG = 0-097 KSVa, mG e = 1 -13 KSVa 2 . 



